In 1895 a first Malay federation under a British protectorate was founded (including the four sultanates Peraq, Selangor, Negri Sembilan, and Pahang). In 1905 a flag was introduced: horizontally white-red-yellow-black (each colour stands for one state, in the order listed here); in the center a lying oval in white with a running tiger. Source: National Geographic 1917. In 1946 other sultanates joined, and the Malay Union was founded, and two years later (1948) it was renamed the Malay Federation. In 1950 a new flag was introduced.
Jan Oskar Engene, 24 June 1996

In 1946 the British decided to do away with the pretence of protectorates and constitute the whole of Malaya / Singapore as a Crown Colony called the Union of Malaya. Very bad move, since face is all in the East. The Malayan Federation in 1948 restored the sultanates as protectorates within a federation with a High Commissioner. Penang, Malacca and Singapore were of course still sovereign British territory but were Settlements within the federation, with Resident Commissioners.
Andrew Yong, 13 November 1999

According to Flaggenbuch 1939, the Federated Malay States used for jack a 1:2 divided per saltire flag, with white, red, black and yellow quarters (the four colours of the national flag).
Ivan Sache, 12 January 2000

I have read that the Federated Malay States' Chief Secretary, was entitled to a defaced Union Jack. Usual white disc surrounded by a green laurel-leaf garland, but no indication of the form of the badge on the disc.
David Prothero, 3 December 1998

From Nick Weekes who was in charge of the display of flags in the Merchant Adventurers' Hall in York in 2001:

When the RCS Library was still in London, I found there a photocopy of an extract from an article The Flags of the Malay Peninsula published in Jour. Straits Branch R. A. Soc., No. 75, 1917 (I think this may be Royal Asian Society). The relevant text said "The Chief Secretary of the Federated Malay States has a Jack corresponding to the Governor's [ie. the Governor of the Straits Settlements as described earlier in the article] in which a kris is the emblem".

Perhaps the reason that I can find no other evidence of this defacement is that the Chief Secretary was getting above himself and was instructed by someone to stop using the defacement. The Chief Secretary was subordinate to the Governor of the Straits Settlements (also High Commissioner for the Malay States and British Agent for British North Borneo and Sarawak).

Perhaps the use of the Federated Malay
States Arms (below) in whole or simply the quartered shield may provide an
alternative possibility?Herman Felani M.Y., 18 December 2003

I have since seen an alternative, but can't remember where. It was an
old-fashioned looking black and white drawing of a kris (Malayan dagger) on a
white disc surrounded by a garland in the centre of a Union Jack. There was no
explanation, but I surmised a Malayan connection from the style of dagger.David Prothero, 19 December 2003

I managed to get an image of the Coat of Arms of the Federated Malay States from
the cover of the book “An Illustrated Guide to the Federated Malay States 1923”
by Cuthbert Woodville Harrison. I could also find at least one use of the Coat
of Arms, used in part as the badge of one
of the volunteer forces of Malaya, ‘the Malayan Volunteer Infantry’, dated 1915,
in “A History of the Singapore Volunteer Corps 1854 – 1937” by Captain T. M.
Winsley of the Singapore Volunteer Corps.Herman Felani M.Y., 18 December 2003

The fourth quarter should be golden-yellow.David Prothero, 19 December 2003